Index

A

average - A

B

basis vectors real C.2.1

bit 1.3

bit-flip operation 2.3.2

Bloch Sphere 3.5.4

bra C.4

bracket A, C.4

C

closed-system evolution 1.4

CNOT gate(see controlled NOT)

commutator 2.3.2,

complex conjugate 2.7.1, B

of a matrix C.3.1, C.3.3

complex number B

computational basis 2.2

controlled NOT 2.6.1, 2.6.2, 5.4, 5.5

controlled phase gate 6.1

controlled unitary operation 2.6.1

D

decoherence 2.1

degenerate C.6

delta

Kronecker C.4

dense coding 5.4

density matrix 3.3,3.5

for two qubits 3.5.2, 3.5.3, 3.5.4

mixed state 3.5

pure state 3.3

density operator E

determinant C.3.6

DiVencenzo's requirements 2.1

Dirac notation C.2.1, C.2.2, C.4

dot product 2.4, C.2.1, E

E

eigenvalue decomposition C.6

eigenvalues C.6

eigenvectors C.6

entangled states (see entanglement)

entanglement 4, 5.4, 1.2.5

pure state 4.2

mixed state 4.3

expectation value 3.6

F

G

group D.2

H

Hadamard gate 2.16

Hamiltonian 3.2

Hermitian matrix 2.4, 3.2, 3.4, 3.5, 8.2, 8.3, C.3.3, C.6.1, E

Hilbert-Schmidt inner product 2.4

I

inner product

for real vectors C.2.1

for complex vectors C.4

inverse of a matrix C.3.7

K

ket 2.5, C.2.2

Kraus operators 8.3

Kronecker delta C.4

Kronecker product C.7

L

local operations 4.2

local unitary transformations 4.2, 4.2.1

M

matrix exponentiation 3.2

maximally entangled states 4.3.1

maximally mixed state 3.5.3

two qubits

mean

median A

mixed state density matrix 3.5

modulus squared B

O

open quantum systems 1.4

open-system evolution 1.4

operator-sum decomposition 8.4

orthogonal 2.4, 3.5.4, 5.2, E

vectors C.4, C.5

P

partial trace

of a Bell state 4.3.1

Pauli matrices 2.4, 3.4, 3.5.4

phase gate 2.3.2

phase-flip 2.3.2

Planck's constant 3.2

projection operator

pure state 3.3, 4.2, E

Q

Qbit (see qubit)

quantum bit 1.3

quantum dense coding (see dense coding)

quantum gates 2.1, 2.3, 2.6

qubit 1.3

R

reduced density operator 4.3.1

of a Bell state 4.3.1

reduced density matrix 4.3.1

see reduced density operator

reduced density operator 4.3.1

requirements for scalable quantum computing 2.1

S

scalability

Schrodinger Equation 3.2

for density matrix 3.3

separable state 4.3

simply separable 4.3

similar matrices C.5

similarity transformation C.5

singular values C.6

special unitary matrix 3.4

spectrum C.6

standard deviation A

SU C.3.8

T

teleportation 5.5

tensor product C.7

trace C.3.5

partial(see partial trace)

transformation 1.3, 2.3, 2.3.1, 2.3.2, 2.4, 2.6, 2.6.1, 2.6.2, 2.7.1, 2.7.2, 3.2, 3.3, 3.4, 3.5.3, 4.2, 4.2, 4.2.1,

active

passive

transpose C.3.2

U

uncertainty principle 5.3

unitary matrix 2.3, C.3.8, D.7.2

universal set of gates 2.6

universality 2.6

V

variance 5.3

X

X-gate 2.3.2

Y

Y-gate 2.3.2

Z

Z-gate 2.3.2